Engineering design often involves the determination of design variable settings to optimize competing performance requirements. In the early design stages we propose narrowing down the domain of design solutions using metamodels of principal components of the multiple performance levels that have been scaled by a multivariate quadratic loss function. The multivariate quadratic loss function is often used as the objective function in reaching optimal solutions because it utilizes the correlation structure of the design's performance metrics and penalizes off-target performance in a symmetrical manner. We also compare the computational performance of these loss-scaled principal components when used to solve for the design with minimal expected multivariate quadratic loss under three modeling approaches: response surface methodology, multivariate adaptive regression splines, and spatial point modeling. We demonstrate the technique on the design of the mechanical frame of an electric vehicle with six desired performance levels determined simultaneously by the dimensions of eight mechanical design elements. The method is the focus in this work.

工程设计通常涉及确定设计变量设置以优化竞争性能要求。在早期设计阶段，我们建议使用由多元二次损失函数缩放的多个性能级别的主要组件的元模型来缩小设计解决方案的范围。多元二次损失函数通常用作达到最佳解决方案的目标函数，因为它利用设计性能指标的相关结构并以对称方式惩罚脱靶性能。我们还比较了这些损失缩放的主成分在三种建模方法下用于求解具有最小预期多元二次损失的设计时的计算性能：响应面方法，多元自适应回归样条和空间点建模。我们展示了电动汽车机械框架设计技术，该技术具有由八个机械设计元素的尺寸同时确定的六个所需性能水平。方法是这项工作的重点。